I've mentioned before that April mean temperatures in Fairbanks are highly correlated with the breakup date at Nenana - see the chart below. The warmest April in Fairbanks history was in 1940, and that year also produced the earliest breakup on record - narrowly ahead of 1998. However, the early breakup of 1940 was quite an outlier for those early decades; 6 of the earliest 7 breakups have occurred since 1990. In the past few decades, it's been more common to see breakup in April than in May, in contrast to earlier years.
Another way of looking at the relationship between breakup and temperature is to calculate the thawing degree days up until the date of breakup. Thawing degree days (TDDs) are the accumulation of temperature excess above freezing; for example, a daily mean temperature of 42°F equates to 10 TDDs. If we add up the daily TDD values for each year between March 1 and the date of breakup, we get the following chart:
The first thing to note is that there is quite wide variation in the amount of thermal energy needed to produce breakup, as measured by TDDs; since 1930, the Fairbanks TDDs have varied from 75 (in 2002) to 265 (in 1975). It's slightly counter-intuitive to see that the latest breakups occur after a relatively small accumulation of TDDs; the reason for this (I believe) is that late breakups allow more time for the increasingly intense solar radiation of May to work on the ice, even though air temperatures are low.
In contrast, if breakup is to occur early, then melting has to be accomplished more by the warmth of the air than by direct solar heating, and so warmer temperatures are required.
We can see that recent decades have been characterized more by early breakups in association with large TDDs, in contrast to earlier years that tended to have smaller TDDs and later breakup. The last two years, 2014 and 2015, were actually a little unusual in having early breakup AND relatively low TDDs - perhaps a consequence of the warm winters and poor ice conditions.
So far this spring Fairbanks is accumulating TDDs more rapidly than in the past 3 years, although it's not a record; in 1965, 45 TDDs were observed already by April 4 (but breakup didn't occur until May 7). According to today's 7-day NWS forecast, Fairbanks will accumulate another 29 TDDs through April 11, putting the total at 59. There doesn't seem to be any sign that the warm weather will abate in subsequent weeks, so the melting rate will probably accelerate in the middle of April, especially as snow cover will be gone by then.
Subjectively, then, it seems we are on pace for something pretty close to a record early breakup, but much will depend on just how warm it is after April 15. I'd say the most likely window for breakup at Nenana is April 21-24; and that's probably close to what everyone else is thinking without any of the temperature analysis. In other words: your guess is as good as mine.